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Talk

Global Nash-Kuiper's theorem to compact manifolds

  • Wentao Cao (Universität Leipzig)
E1 05 (Leibniz-Saal)

Abstract

In this talk, I will present some recent results regarding isometric embedding. I first review some conclusions on $C^{1,\theta}$ isometric immersions and isometric extension and related problem. Then I will show our global extensions of the celebrated Nash-Kuiper theorem for $C^{1,\theta}$ isometric immersions of compact manifolds with optimal H\"older exponent. In particular for the Weyl problem of isometrically embedding a convex compact surface in 3-space, we show that the Nash-Kuiper non-rigidity prevails upto exponent $\theta<1/5$. This extends previous results on embedding 2-discs as well as higher dimensional analogues. The presented results are joint work with my mentor Prof. Dr. Szekelyhidi in Leipzig University.

Upcoming Events of this Seminar

  • Monday, 14.07.25 tba with Alexandra Holzinger
  • Tuesday, 15.07.25 tba with Anna Shalova
  • Friday, 15.08.25 tba with Thomas Suchanek
  • Friday, 22.08.25 tba with Nikolay Barashkov
  • Friday, 29.08.25 tba with Andreas Koller